Archiv der Mathematik

, Volume 73, Issue 6, pp 465–473

Random projections of regular polytopes


  • K. Böröczky, Jr.
    • Mathematical Institute of the, Hungarian Academy of Sciences, H-1364 Budapest, P.O.B. 127, Hungary
  • M. Henk
    • University of Magdeburg, Department of Mathematics/IMO, Universitätsplatz 2, D-39106 Magdeburg, Germany

DOI: 10.1007/s000130050424

Cite this article as:
Böröczky, Jr., K. & Henk, M. Arch. Math. (1999) 73: 465. doi:10.1007/s000130050424


Based on an approach of Affentranger & Schneider we give an asymptotic formula for the expected number of k-faces of the orthogonal projection of a regular n-crosspolytope onto a randomly chosen isotropic subspace of fixed dimension, as n tends to infinity. In particular, we present a precise asymptotic formula for the (spherical) volume of spherical regular simplices, which generalizes Daniel's formula.

Copyright information

© Birkhäuser Verlag, Basel 1999